Value of the Siemens Mercury Unit of Electrical Resistance. 163 



To form the equation of motion of the needle, we can proceed 

 the rest of the way as Maxwell has done (Electricity, art. 762). 

 Assuming that all frictional resistances to the needle are propor- 

 tional to the velocity of the needles, we have 



B g? + C*+D,«,I, .... (2) 



where B, C, and D are constants. 



Eliminating I between this equation and (1), we find 



(»^5)(B? + 0* + B.) + ^^ • • (3) 



At first sight this equation will appear to be the same as that of 

 Maxwell ; but on further examination we see that it is more 

 general in the value of q. 



Equation (3) is the correct equatiou to use in this case, and 

 reduces to that of Kohlrausch when L = 0. 



To see how this error will affect Kohlrausch's results, we must 

 remember that he uses this equation to find the constant of his 

 galvanometer, on which his whole experiment depends ; and the 

 error is so interwoven with all his results that an entire recom- 

 putation is necessary, provided the data for calculating the co- 

 efficient of self-induction of the galvanometer coils and earth 

 inductor can be obtained. 



The equation 



does not hold when self-induction is considered ; and so his fun- 

 damental equation (1) is not correct, containing a twofold error. 



The linear differential equation (3) is easily solved ; but as the 

 results are complicated, it is hardly worth while at present, until 

 a recalculation can be made. 1 prefer to solve it on the suppo- 

 sition that L is small, and thus merely obtain a correction to 

 Kohlrausch's equation connecting t and t , after which equa- 

 tion (15) or (17) (Maxwell's 'Electricity/ art. 762) can be used 

 when made more general by substituting q for Gra. 



As far as I have had time to go at present, the correction 

 seems to be in the direction of making Kohlrausch's determina- 

 tion more nearly coincide with that of the Committee on Elec- 

 trical Standards of the British Association. Other engagements 

 occupy my attention at present ; but I hope to see these correc- 

 tions made to an otherwise excellent determination of this most 

 important unit. 



London, August 4, 1875. 



M 2 



